Controllability of a Fluid-Structure Interaction System Governed by the Heat and Damped Beam Equations

TL;DR

This paper investigates the controllability and observability of a 2D fluid-structure interaction system governed by heat and damped beam equations, establishing Carleman estimates and inequalities for various damping regimes.

Contribution

It introduces a global Carleman estimate for the coupled system and analyzes controllability properties considering different damping parameters.

Findings

Established a global Carleman estimate for the coupled system

Derived inequalities for the beam equation under various damping regimes

Analyzed null-controllability and observability properties

Abstract

In this article, we study the null-controllability and observability properties of a bi-dimensio\-nal fluid-structure interaction system, governed by the heat equation coupled with the damped beam equation. To do so, we prove a global Carleman estimate for the coupled system, making explicit the dependence on the damping parameter. In the course of the study, we demonstrate several inequalities for the beam equation alone, valid for different damping parameter regimes.